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Annotation 2961809476876

#PATH

But in order for this to happen, Jupyter needs to know where to look for the associated executable: that is, it needs to know which path the python sits in.

These paths are specified in jupyter's kernelspec, and it's possible for the user to adjust them to their desires.
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Running Jupyter with multiple Python and IPython paths - Stack Overflow
for a non-existent Python version. Jupyter is set-up to be able to use a wide range of "kernels", or execution engines for the code. These can be Python 2, Python 3, R, Julia, Ruby... there are dozens of possible kernels to use. <span>But in order for this to happen, Jupyter needs to know where to look for the associated executable: that is, it needs to know which path the python sits in. These paths are specified in jupyter's kernelspec , and it's possible for the user to adjust them to their desires. For example, here's the list of kernels that I have on my system: $ jupyter kernelspec list Available kernels: python2.7 /Users/jakevdp/.ipython/kernels/python2.7 python3.



Annotation 2961839361292

#betancourt #probability-theory
In particular, many introductions to probability theory sloppily confound the abstract mathematics with their practical implementations, convoluting what we can calculate in the theory with how we perform those calculations. To make matters even worse, probability theory is used to model a variety of subtlety different systems, which then burdens the already confused mathematics with the distinct and often conflicting philosophical connotations of those applications.
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Probability Theory (For Scientists and Engineers)
ity theory is a rich and complex field of mathematics with a reputation for being confusing if not outright impenetrable. Much of that intimidation, however, is due not to the abstract mathematics but rather how they are employed in practice. <span>In particular, many introductions to probability theory sloppily confound the abstract mathematics with their practical implementations, convoluting what we can calculate in the theory with how we perform those calculations. To make matters even worse, probability theory is used to model a variety of subtlety different systems, which then burdens the already confused mathematics with the distinct and often conflicting philosophical connotations of those applications. In this case study I attempt to untangle this pedagogical knot to illuminate the basic concepts and manipulations of probability theory. Our ultimate goal is to demystify what we can



Annotation 2961841458444

#betancourt #probability-theory
we cannot explicitly construct abstract probability distributions in any meaningful sense. Instead we must utilize problem-specific representations of abstract probability distributions
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Probability Theory (For Scientists and Engineers)
robability theory. Let me open with a warning that the section on abstract probability theory will be devoid of any concrete examples. This is not because of any conspiracy to confuse the reader, but rather is a consequence of the fact that <span>we cannot explicitly construct abstract probability distributions in any meaningful sense. Instead we must utilize problem-specific representations of abstract probability distributions which means that concrete examples will have to wait until we introduce these representations in Section 3. 1 Setting A Foundation Ultimately probability theory concerns itself wi



Annotation 2961848012044

#best-practice #pystan
When they do fail, however, their failures manifest in diagnostics that are readily checked.
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pystan_workflow
emented with responsibility. In particular, while dynamic implementations of Hamiltonian Monte Carlo, i.e. implementations where the integration time is dynamic, do perform well over a large class of models their success is not guaranteed. <span>When they do fail, however, their failures manifest in diagnostics that are readily checked. By acknowledging and respecting these diagnostics you can ensure that Stan is accurately fitting the Bayesian posterior and hence accurately characterizing your model. And only with



Annotation 2961850371340

#best-practice #pystan
the effective sample size quantifies the accuracy of the Markov chain Monte Carlo estimator of a given function, here each parameter mean, provided that geometric ergodicity holds. The potential problem with these effective sample sizes, however, is that we must estimate them from the fit output. When we geneate less than 0.001 effective samples per transition of the Markov chain the estimators that we use are typically biased and can significantly overestimate the true effective sample size.
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pystan_workflow
chains (at convergence, Rhat=1). We can investigate each more programatically, however, using some of our utility functions. Checking Split R̂ R^ and Effective Sample Sizes¶ As noted in Section 1, <span>the effective sample size quantifies the accuracy of the Markov chain Monte Carlo estimator of a given function, here each parameter mean, provided that geometric ergodicity holds. The potential problem with these effective sample sizes, however, is that we must estimate them from the fit output. When we geneate less than 0.001 effective samples per transition of the Markov chain the estimators that we use are typically biased and can significantly overestimate the true effective sample size. We can check that our effective sample size per iteration is large enough with one of our utility functions, In [14]: stan_utility.check_n_eff(fit)



Annotation 2961851944204

#best-practice #pystan
Split \( \hat{R} \) quantifies an important necessary condition for geometric ergodicity
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Annotation 2961853517068

#best-practice #pystan
Both large split R ̂ R^ \hat{R} and low effective sample size per iteration are consequences of poorly mixing Markov chains. Improving the mixing of the Markov chains almost always requires tweaking the model specification, for example with a reparameterization or stronger priors.
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Annotation 2961855614220

#best-practice #pystan
The dynamic implementation of Hamiltonian Monte Carlo used in Stan has a maximum trajectory length built in to avoid infinite loops that can occur for non-identified models. For sufficiently complex models, however, Stan can saturate this threshold even if the model is identified, which limits the efficacy of the sampler.
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pystan_workflow
agnostics that can indicate problems with the fit. These diagnostics are extremely sensitive and typically indicate problems long before the arise in the more universal diagnostics considered above. Checking the Tree Depth¶ <span>The dynamic implementation of Hamiltonian Monte Carlo used in Stan has a maximum trajectory length built in to avoid infinite loops that can occur for non-identified models. For sufficiently complex models, however, Stan can saturate this threshold even if the model is identified, which limits the efficacy of the sampler. We can check whether that threshold was hit using one of our utility functions, In [17]: stan_utility.check_treedepth(fit) 0 of 4000 iterat



Annotation 2961857187084

#best-practice #pystan

Hamiltonian Monte Carlo proceeds in two phases -- the algorithm first simulates a Hamiltonian trajectory that rapidly explores a slice of the target parameter space before resampling the auxiliary momenta to allow the next trajectory to explore another slice of the target parameter space. Unfortunately, the jumps between these slices induced by the momenta resamplings can be short, which often leads to slow exploration.

We can identify this problem by consulting the energy Bayesian Fraction of Missing Information,
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.sampling(data=data, seed=194838, control=dict(max_treedepth=15)) and then check if still saturated this larger threshold with stan_utility.check_treedepth(fit, 15) Checking the E-BFMI¶ <span>Hamiltonian Monte Carlo proceeds in two phases -- the algorithm first simulates a Hamiltonian trajectory that rapidly explores a slice of the target parameter space before resampling the auxiliary momenta to allow the next trajectory to explore another slice of the target parameter space. Unfortunately, the jumps between these slices induced by the momenta resamplings can be short, which often leads to slow exploration. We can identify this problem by consulting the energy Bayesian Fraction of Missing Information, In [18]: stan_utility.check_energy(fit) Chain 2: E-BFMI = 0.177681346951 E-BFMI below 0.2 indicates you may need to reparameterize your mod



Annotation 2961858759948

#best-practice #pystan
The stan_utility module uses the threshold of 0.2 to diagnose problems
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ction of Missing Information, In [18]: stan_utility.check_energy(fit) Chain 2: E-BFMI = 0.177681346951 E-BFMI below 0.2 indicates you may need to reparameterize your model <span>The stan_utility module uses the threshold of 0.2 to diagnose problems, although this is based on preliminary empirical studies and should be taken only as a very rough recommendation. In particular, this diagnostic comes out of recent theoretical work an



Annotation 2961860332812

#best-practice #pystan
divergences indicate pathological neighborhoods of the posterior that the simulated Hamiltonian trajectories are not able to explore sufficiently well.
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pystan_workflow
ow E-BFMI are remedied by tweaking the specification of the model. Unfortunately the exact tweaks required depend on the exact structure of the model and, consequently, there are no generic solutions. Checking Divergences¶ <span>Finally, we can check divergences which indicate pathological neighborhoods of the posterior that the simulated Hamiltonian trajectories are not able to explore sufficiently well. For this fit we have a significant number of divergences In [19]: stan_utility.check_div(fit) 202.0 of 4000 iterations ended with a divergen



Annotation 2961861905676

#best-practice #pystan

Divergences, however, can sometimes be false positives. To verify that we have real fitting issues we can rerun with a larger target acceptance probability, adapt_delta, which will force more accurate simulations of Hamiltonian trajectories and reduce the false positives.

In [20]: 

         

	  

    		
  


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nce (5.05%)
  Try running with larger adapt_delta to remove the divergences
 
 
 

 
 

 
 
 
 
 
 
 indicating that the Markov chains did not completely explore the posterior and that our Markov chain Monte Carlo estimators will be biased. 
 <span>Divergences, however, can sometimes be false positives.  To verify that we have real fitting issues we can rerun with a larger target acceptance probability,  adapt_delta , which will force more accurate simulations of Hamiltonian trajectories and reduce the false positives. 

 
 
 
 
 
 In [20]: 
 
     
 fit = model.sampling(data=data, seed=194838, control=dict(adapt_delta=0.9))
 

 
 
 

 
 
 
 
 
 
 Checking again, 

 
 
 
 
 
 In [21]: 
 
     
 sampler_params = fit.get_sam



Annotation 2961863478540

  

    
                 
      
      
         #best-practice #pystan
         

              
	  

  		 
            
          In order to argue that divergences are only false positives, the divergences have to be completely eliminated for some adapt_delta sufficiently close to 1.
         

	  

    		
  


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 45.0 of 4000 iterations ended with a divergence (1.125%)
  Try running with larger adapt_delta to remove the divergences
 
 
 

 
 

 
 
 
 
 
 
 we see that while the divergences were reduced they did not completely vanish.  <span>In order to argue that divergences are only false positives, the divergences have to be completely eliminated for some  adapt_delta  sufficiently close to 1.  Here we could continue increasing  adapt_delta , where we would see that the divergences do not completely vanish, or we can analyze the existing divergences graphically. 
 If the dive



Annotation 2961865051404

  

    
                 
      
      
         #best-practice #pystan
         

              
	  

  		 
            
          
If the divergences are not false positives then they will tend to concentrate in the pathological neighborhoods of the posterior. Falsely positive divergent iterations, however, will follow the same distribution as non-divergent iterations.



         

	  

    		
  


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ompletely eliminated for some  adapt_delta  sufficiently close to 1.  Here we could continue increasing  adapt_delta , where we would see that the divergences do not completely vanish, or we can analyze the existing divergences graphically. 
 <span>If the divergences are not false positives then they will tend to concentrate in the pathological neighborhoods of the posterior.  Falsely positive divergent iterations, however, will follow the same distribution as non-divergent iterations. 
 Here we will use the  partition_div  function of the  stan_utility  module to separate divergence and non-divergent iterations, but note that this function works only if your model pa



Annotation 2961866624268

  

    
                 
      
      
         #best-practice #pystan
         

              
	  

  		 
            
          One of the challenges with a visual analysis of divergences is determining exactly which parameters to examine. Consequently visual analyses are most useful when there are already components of the model about which you are suspicious
         

	  

    		
  


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      color = green, alpha=0.5)

plot.gca().set_xlabel("theta_1")
plot.gca().set_ylabel("tau")

plot.show()
 

 
 
 

 
 


 
 
 WARNING:root:`dtypes` ignored when `permuted` is False.
 
 
 

 


 

 

 

 
 

 
 
 
 
 
 
 <span>One of the challenges with a visual analysis of divergences is determining exactly which parameters to examine.  Consequently visual analyses are most useful when there are already components of the model about which you are suspicious, as in this case where we know that the correlation between random effects ( theta_1  through  theta_8 ) and the hierarchical standard deviation,  tau , can be problematic. 
 Indeed we 



Annotation 2961868197132

  

    
                 
      
      
         #best-practice #pystan
         

              
	  

  		 
            
          In order to avoid this issue we have to consider a modification to our model, and in this case we can appeal to a non-centered parameterization of the same model that does not suffer these issues.
         

	  

    		
  


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be problematic. 
 Indeed we see the divergences clustering towards small values of tau where the posterior abruptly stops.  This abrupt stop is indicative of a transition into a pathological neighborhood that Stan was not able to penetrate. 
 <span>In order to avoid this issue we have to consider a modification to our model, and in this case we can appeal to a non-centered parameterization of the same model that does not suffer these issues. 

 
 
 
 
 
 
 
 
 A Successful Fit¶ Multiple diagnostics have indicated that our fit of the centered parameterization of our hierarchical model is not to be trusted, so let's instead c



Annotation 2961872391436

  

    
                 
      
      
         #Rochford #best-practice #pymc
         

              
	  

  		 
            
          Since December 2014, I have tracked the books I read in a Google spreadsheet.
         

	  

    		
  


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Austin Rochford - Quantifying Three Years of Reading
s About Projects Talks Reading Log 
                    
                 
             
        
         
             
                 
                     
     Quantifying Three Years of Reading 
     Posted on December 29, 2017  
 


 <span>Since December 2014, I have tracked the books I read in a Google spreadsheet. It recently occurred to me to use this data to quantify how my reading habits have changed over time. This post will use PyMC3 to model my reading habits. 
 %matplotlib inline 
 from it



Flashcard 2961873964300

    
	

	    
Tags

	    
#Rochford #best-practice #pymc

	

    

    

    

    
	

	    
Question

	    
Since December 2014, I have tracked the books I read in a [...].

	

    

    

    
	

	    
Answer

	    

		Google spreadsheet
	    

	

    




statusnot learnedmeasured difficulty37% [default]last interval [days]               
repetition number in this series0memorised on               scheduled repetition               
scheduled repetition interval               last repetition or drill
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                    Since December 2014, I have tracked the books I read in a Google spreadsheet. 

Original toplevel document
Austin Rochford - Quantifying Three Years of Reading
s About Projects Talks Reading Log 
                    
                 
             
        
         
             
                 
                     
     Quantifying Three Years of Reading 
     Posted on December 29, 2017  
 


 <span>Since December 2014, I have tracked the books I read in a Google spreadsheet. It recently occurred to me to use this data to quantify how my reading habits have changed over time. This post will use PyMC3 to model my reading habits. 
 %matplotlib inline 
 from it






Flashcard 2961875537164

    
	

	    
Tags

	    
#PATH

	

    

    

    

    
	

	    
Question

	    
When you type any command at the prompt (say, python), the system has a [...] that it looks for the executable. 

	

    

    

    
	

	    
Answer

	    

		well-defined sequence of places
	    

	

    




statusnot learnedmeasured difficulty37% [default]last interval [days]               
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scheduled repetition interval               last repetition or drill
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                    When you type any command at the prompt (say,  python ), the system has a well-defined sequence of places that it looks for the executable. This sequence is defined in a system variable called  PATH , which the user can specify. To see your  PATH , you can type  echo $PATH .   
</spa
Original toplevel document
Running Jupyter with multiple Python and IPython paths - Stack Overflow
thon installs and finds packages How Jupyter knows what Python to use 

 For the sake of completeness, I'll try to do a quick ELI5 on each of these, so you'll know how to solve this issue in the best way for you. 

 1. Unix/Linux/OSX $PATH 

 <span>When you type any command at the prompt (say,  python ), the system has a well-defined sequence of places that it looks for the executable. This sequence is defined in a system variable called  PATH , which the user can specify. To see your  PATH , you can type  echo $PATH . 

 The result is a list of directories on your computer, which will be searched  in order  for the desired executable. From your output above, I assume that it contains this:  

 $ echo






Flashcard 2961877896460

    
	

	    
Tags

	    
#PATH

	

    

    

    

    
	

	    
Question

	    
To see your PATH, you can type [...]



 

	

    

    

    
	

	    
Answer

	    

		echo $PATH.
	    

	

    




statusnot learnedmeasured difficulty37% [default]last interval [days]               
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mmand at the prompt (say,  python ), the system has a well-defined sequence of places that it looks for the executable. This sequence is defined in a system variable called  PATH , which the user can specify. To see your  PATH , you can type  <span>echo $PATH .   
<span><body><html>
Original toplevel document
Running Jupyter with multiple Python and IPython paths - Stack Overflow
thon installs and finds packages How Jupyter knows what Python to use 

 For the sake of completeness, I'll try to do a quick ELI5 on each of these, so you'll know how to solve this issue in the best way for you. 

 1. Unix/Linux/OSX $PATH 

 <span>When you type any command at the prompt (say,  python ), the system has a well-defined sequence of places that it looks for the executable. This sequence is defined in a system variable called  PATH , which the user can specify. To see your  PATH , you can type  echo $PATH . 

 The result is a list of directories on your computer, which will be searched  in order  for the desired executable. From your output above, I assume that it contains this:  

 $ echo






Flashcard 2961880255756

    
	

	    
Tags

	    
#PATH

	

    

    

    

    
	

	    
Question

	    
The result of echo $PATH  is [...]

	

    

    

    
	

	    
Answer

	    

		a list of directories on your computer
	    

	

    




statusnot learnedmeasured difficulty37% [default]last interval [days]               
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Open it

                    The result is a list of directories on your computer, which will be searched  in order  for the desired executable. 

Original toplevel document
Running Jupyter with multiple Python and IPython paths - Stack Overflow
mpt (say,  python ), the system has a well-defined sequence of places that it looks for the executable. This sequence is defined in a system variable called  PATH , which the user can specify. To see your  PATH , you can type  echo $PATH . 

 <span>The result is a list of directories on your computer, which will be searched  in order  for the desired executable. From your output above, I assume that it contains this:  

 $ echo $PATH
/usr/bin/:/Library/Frameworks/Python.framework/Versions/3.5/bin/:/usr/local/bin/ 

 In windows  echo %path% 

 P






Flashcard 2961883401484

    
	

	    
Tags

	    
#PATH

	

    

    

    

    
	

	    
Question

	    
When you run python and do something like import matplotlib, Python has [...] that specifies where to find the package you want

	

    

    

    
	

	    
Answer

	    

		sys.path
	    

	

    




statusnot learnedmeasured difficulty37% [default]last interval [days]               
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scheduled repetition interval               last repetition or drill
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Open it

                    When you run python and do something like  import matplotlib , Python has to play a similar game to find the package you have in mind. Similar to  $PATH  in unix, Python has  sys.path  that specifies these 

Original toplevel document
Running Jupyter with multiple Python and IPython paths - Stack Overflow
 many installations of the same program on your system. Changing the path is not too complicated; see e.g. How to permanently set $PATH on Linux?. 

 Windows - How to set environment variables in Windows 10  

 2. How Python finds packages 

 <span>When you run python and do something like  import matplotlib , Python has to play a similar game to find the package you have in mind. Similar to  $PATH  in unix, Python has  sys.path  that specifies these: 

 $ python
>>> import sys
>>> sys.path
['',
 '/Users/jakevdp/anaconda/lib/python3.5', 
 '/Users/jakevdp/anaconda/lib/python3.5/site-packages',
 ...] 

 Some importan






Flashcard 2961885760780

    
	

	    
Tags

	    
#PATH

	

    

    

    

    
	

	    
Question

	    
When you run python and do something like import matplotlib, Python has sys.paththat specifies  [...]

	

    

    

    
	

	    
Answer

	    

		where to find the package you want
	    

	

    




statusnot learnedmeasured difficulty37% [default]last interval [days]               
repetition number in this series0memorised on               scheduled repetition               
scheduled repetition interval               last repetition or drill
Parent (intermediate) annotation
Open it

                    When you run python and do something like  import matplotlib , Python has to play a similar game to find the package you have in mind. Similar to  $PATH  in unix, Python has  sys.path  that specifies these 

Original toplevel document
Running Jupyter with multiple Python and IPython paths - Stack Overflow
 many installations of the same program on your system. Changing the path is not too complicated; see e.g. How to permanently set $PATH on Linux?. 

 Windows - How to set environment variables in Windows 10  

 2. How Python finds packages 

 <span>When you run python and do something like  import matplotlib , Python has to play a similar game to find the package you have in mind. Similar to  $PATH  in unix, Python has  sys.path  that specifies these: 

 $ python
>>> import sys
>>> sys.path
['',
 '/Users/jakevdp/anaconda/lib/python3.5', 
 '/Users/jakevdp/anaconda/lib/python3.5/site-packages',
 ...] 

 Some importan






Flashcard 2961887595788

    
	

	    
Tags

	    
#PATH

	

    

    

    

    
	

	    
Question

	    
by default, the first entry in sys.path is [...].

	

    

    

    
	

	    
Answer

	    

		the current directory
	    

	

    




statusnot learnedmeasured difficulty37% [default]last interval [days]               
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                    by default, the first entry in  sys.path  is the current directory. 

Original toplevel document
Running Jupyter with multiple Python and IPython paths - Stack Overflow
nix, Python has  sys.path  that specifies these: 

 $ python
>>> import sys
>>> sys.path
['',
 '/Users/jakevdp/anaconda/lib/python3.5', 
 '/Users/jakevdp/anaconda/lib/python3.5/site-packages',
 ...] 

 Some important things: <span>by default, the first entry in  sys.path  is the current directory. Also, unless you modify this (which you shouldn't do unless you know exactly what you're doing) you'll usually find something called  site-packages  in the path: this is the default pla






Flashcard 2961889168652

    
	

	    
Tags

	    
#PATH

	

    

    

    

    
	

	    
Question

	    
the default place that Python puts packages is something called [...]

	

    

    

    
	

	    
Answer

	    

		site-packages



when you install them using python setup.py install, or pip, or conda, or a similar means

 
	    

	

    




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                    is the current directory. Also, unless you modify this (which you shouldn't do unless you know exactly what you're doing) you'll usually find something called  site-packages  in the path: this is the default place that Python puts packages when you install them using  python setup.py install , or  pip , or  conda , or a similar means. 

Original toplevel document
Running Jupyter with multiple Python and IPython paths - Stack Overflow
these: 

 $ python
>>> import sys
>>> sys.path
['',
 '/Users/jakevdp/anaconda/lib/python3.5', 
 '/Users/jakevdp/anaconda/lib/python3.5/site-packages',
 ...] 

 Some important things: by default, the first entry in  sys.path  <span>is the current directory. Also, unless you modify this (which you shouldn't do unless you know exactly what you're doing) you'll usually find something called  site-packages  in the path: this is the default place that Python puts packages when you install them using  python setup.py install , or  pip , or  conda , or a similar means. 

 The important thing to note is that  each python installation has its own site-packages , where packages are installed  for that specific Python version . In other words, if you inst






Flashcard 2961891527948

    
	

	    
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#PATH

	

    

    

    

    
	

	    
Question

	    
some Python packages come bundled with stand-alone scripts that you can run from [...]

	

    

    

    
	

	    
Answer

	    

		the command line



(examples are pip, ipython, jupyter, pep8, etc.)
	    

	

    




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                    some Python packages come bundled with stand-alone scripts that you can run from the command line (examples are  pip ,  ipython ,  jupyter ,  pep8 , etc.) By default, these executables will be put in the  same directory path  as the Python used to install them, and are designed to w
Original toplevel document
Running Jupyter with multiple Python and IPython paths - Stack Overflow
cause it was installed on a different Python! This is why in our twitter exchange I recommended you focus on one Python installation, and fix your $PATH  so that you're only using the one you want to use. 

 There's another component to this: <span>some Python packages come bundled with stand-alone scripts that you can run from the command line (examples are  pip ,  ipython ,  jupyter ,  pep8 , etc.) By default, these executables will be put in the  same directory path  as the Python used to install them, and are designed to work  only with that Python installation . 

 That means that, as your system is set-up, when you run  python , you get  /usr/bin/python , but when you run  ipython , you get  /Library/Frameworks/Python.framework/Versions/3.5/bi






Flashcard 2961893887244

    
	

	    
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#PATH

	

    

    

    

    
	

	    
Question

	    
some Python packages come bundled with  [...]  that you can run from the command line

	

    

    

    
	

	    
Answer

	    

		stand-alone scripts



(examples are pip, ipython, jupyter, pep8, etc.)
	    

	

    




statusnot learnedmeasured difficulty37% [default]last interval [days]               
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                    some Python packages come bundled with stand-alone scripts that you can run from the command line (examples are  pip ,  ipython ,  jupyter ,  pep8 , etc.) By default, these executables will be put in the  same directory path  as the Python used to install them, and are designed to w
Original toplevel document
Running Jupyter with multiple Python and IPython paths - Stack Overflow
cause it was installed on a different Python! This is why in our twitter exchange I recommended you focus on one Python installation, and fix your $PATH  so that you're only using the one you want to use. 

 There's another component to this: <span>some Python packages come bundled with stand-alone scripts that you can run from the command line (examples are  pip ,  ipython ,  jupyter ,  pep8 , etc.) By default, these executables will be put in the  same directory path  as the Python used to install them, and are designed to work  only with that Python installation . 

 That means that, as your system is set-up, when you run  python , you get  /usr/bin/python , but when you run  ipython , you get  /Library/Frameworks/Python.framework/Versions/3.5/bi






Flashcard 2961896508684

    
	

	    
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some Python packages that you can run from the command line (examples are pip, ipython, jupyter, pep8, etc.) are put in [...where...]

	

    

    

    
	

	    
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		the same directory path as the Python used to install them
	    

	

    




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                    some Python packages come bundled with stand-alone scripts that you can run from the command line (examples are  pip ,  ipython ,  jupyter ,  pep8 , etc.) By default, these executables will be put in the  same directory path  as the Python used to install them, and are designed to work  only with that Python installation . 
<html>
Original toplevel document
Running Jupyter with multiple Python and IPython paths - Stack Overflow
cause it was installed on a different Python! This is why in our twitter exchange I recommended you focus on one Python installation, and fix your $PATH  so that you're only using the one you want to use. 

 There's another component to this: <span>some Python packages come bundled with stand-alone scripts that you can run from the command line (examples are  pip ,  ipython ,  jupyter ,  pep8 , etc.) By default, these executables will be put in the  same directory path  as the Python used to install them, and are designed to work  only with that Python installation . 

 That means that, as your system is set-up, when you run  python , you get  /usr/bin/python , but when you run  ipython , you get  /Library/Frameworks/Python.framework/Versions/3.5/bi






Flashcard 2961898867980

    
	

	    
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#PATH

	

    

    

    

    
	

	    
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the $PATH variable are usually set in[...files...]

	

    

    

    
	

	    
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		shell.dotfiles



~/.zshrc or ~/.bashrc,or ~/.bash_profile
	    

	

    




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                    Well, first make sure your  $PATH  variable is doing what you want it to. You likely have a startup script called something like  ~/.bash_profile  or  ~/.bashrc  that sets this  $PATH  variable. 

Original toplevel document
Running Jupyter with multiple Python and IPython paths - Stack Overflow
s that the packages you can import when running  python  are entirely separate from the packages you can import when running  ipython  or a Jupyter notebook: you're using two completely independent Python installations. 

 So how to fix this? <span>Well, first make sure your  $PATH  variable is doing what you want it to. You likely have a startup script called something like  ~/.bash_profile  or  ~/.bashrc  that sets this  $PATH  variable. On Windows, you can modify the user specific environment variables. You can manually modify that if you want your system to search things in a different order. When you first install an






Flashcard 2961901227276

    
	

	    
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jupyter uses [...]to look for the associated kernels

	

    

    

    
	

	    
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		kernelspec
	    

	

    




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                    But in order for this to happen, Jupyter needs to know where to look for the associated executable: that is, it needs to know which path the  python  sits in.   These paths are specified in jupyter's  kernelspec , and it's possible for the user to adjust them to their desires. 
<html>
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Running Jupyter with multiple Python and IPython paths - Stack Overflow
 for a non-existent Python version. 

 Jupyter is set-up to be able to use a wide range of "kernels", or execution engines for the code. These can be Python 2, Python 3, R, Julia, Ruby... there are dozens of possible kernels to use. <span>But in order for this to happen, Jupyter needs to know where to look for the associated executable: that is, it needs to know which path the  python  sits in. 

 These paths are specified in jupyter's  kernelspec , and it's possible for the user to adjust them to their desires. For example, here's the list of kernels that I have on my system: 

 $ jupyter kernelspec list
Available kernels:
  python2.7        /Users/jakevdp/.ipython/kernels/python2.7
  python3.






Flashcard 2961903586572

    
	

	    
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IPython relies on [...package...] to install a python kernel

	

    

    

    
	

	    
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                    IPython relies on the ipykernel package which contains a command to install a python kernel: for example    $ python - m ipykernel install    It will create a kernelspec associated with the Python executable you use to run th
Original toplevel document
Running Jupyter with multiple Python and IPython paths - Stack Overflow
 specifies the kernel name, the path to the executable, and other relevant info.
You can adjust kernels manually, editing the metadata inside the directories listed above. 

 The command to install a kernel can change depending on the kernel. <span>IPython relies on the ipykernel package which contains a command to install a python kernel: for example 

 $  python -m ipykernel install 

 It will create a kernelspec associated with the Python executable you use to run this command. You can then choose this kernel in the Jupyter notebook to run your code with that Python. 

 You can see other options that ipykernel provides using the help command: 

 $ python -m ipykernel install --help
usage: ipython-kernel-install [-h] [--user] [--name NAME]
          






Flashcard 2961906732300

    
	

	    
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Ipython uses 



 $ python - m ipykernel install 



 to create a [...] associated with the Python executable you use to run this command. 

	

    

    

    
	

	    
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		kernelspec

 

You can then choose this kernel in the Jupyter notebook to run your code with that Python.

	    

	

    




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                    IPython relies on the ipykernel package which contains a command to install a python kernel: for example    $ python - m ipykernel install    It will create a kernelspec associated with the Python executable you use to run this command. You can then choose this kernel in the Jupyter notebook to run your code with that Python.   
</h
Original toplevel document
Running Jupyter with multiple Python and IPython paths - Stack Overflow
 specifies the kernel name, the path to the executable, and other relevant info.
You can adjust kernels manually, editing the metadata inside the directories listed above. 

 The command to install a kernel can change depending on the kernel. <span>IPython relies on the ipykernel package which contains a command to install a python kernel: for example 

 $  python -m ipykernel install 

 It will create a kernelspec associated with the Python executable you use to run this command. You can then choose this kernel in the Jupyter notebook to run your code with that Python. 

 You can see other options that ipykernel provides using the help command: 

 $ python -m ipykernel install --help
usage: ipython-kernel-install [-h] [--user] [--name NAME]
          






Flashcard 2961910140172

    
	

	    
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#best-practice #pystan

	

    

    

    

    
	

	    
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divergences indicate [...] that the simulated Hamiltonian trajectories are not able to explore sufficiently well.

	

    

    

    
	

	    
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		pathological neighborhoods of the posterior
	    

	

    




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                    divergences indicate pathological neighborhoods of the posterior that the simulated Hamiltonian trajectories are not able to explore sufficiently well. 

Original toplevel document
pystan_workflow
ow E-BFMI are remedied by tweaking the specification of the model.  Unfortunately the exact tweaks required depend on the exact structure of the model and, consequently, there are no generic solutions. 

 
 
 
 
 
 
 
 
 Checking Divergences¶ <span>Finally, we can check divergences which indicate pathological neighborhoods of the posterior that the simulated Hamiltonian trajectories are not able to explore sufficiently well.  For this fit we have a significant number of divergences 

 
 
 
 
 
 In [19]: 
 
     
 stan_utility.check_div(fit)
 

 
 
 

 
 


 
 
 202.0 of 4000 iterations ended with a divergen






Flashcard 2961911713036

    
	

	    
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#best-practice #pystan

	

    

    

    

    
	

	    
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divergences indicate pathological neighborhoods of the posterior that [...] are not able to explore sufficiently well.

	

    

    

    
	

	    
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		the simulated Hamiltonian trajectories
	    

	

    




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                    divergences indicate pathological neighborhoods of the posterior that the simulated Hamiltonian trajectories are not able to explore sufficiently well. 

Original toplevel document
pystan_workflow
ow E-BFMI are remedied by tweaking the specification of the model.  Unfortunately the exact tweaks required depend on the exact structure of the model and, consequently, there are no generic solutions. 

 
 
 
 
 
 
 
 
 Checking Divergences¶ <span>Finally, we can check divergences which indicate pathological neighborhoods of the posterior that the simulated Hamiltonian trajectories are not able to explore sufficiently well.  For this fit we have a significant number of divergences 

 
 
 
 
 
 In [19]: 
 
     
 stan_utility.check_div(fit)
 

 
 
 

 
 


 
 
 202.0 of 4000 iterations ended with a divergen






Flashcard 2961913285900

    
	

	    
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#best-practice #pystan

	

    

    

    

    
	

	    
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[...] indicate pathological neighborhoods of the posterior that the simulated Hamiltonian trajectories are not able to explore sufficiently well.

	

    

    

    
	

	    
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		divergences
	    

	

    




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                    divergences indicate pathological neighborhoods of the posterior that the simulated Hamiltonian trajectories are not able to explore sufficiently well. 

Original toplevel document
pystan_workflow
ow E-BFMI are remedied by tweaking the specification of the model.  Unfortunately the exact tweaks required depend on the exact structure of the model and, consequently, there are no generic solutions. 

 
 
 
 
 
 
 
 
 Checking Divergences¶ <span>Finally, we can check divergences which indicate pathological neighborhoods of the posterior that the simulated Hamiltonian trajectories are not able to explore sufficiently well.  For this fit we have a significant number of divergences 

 
 
 
 
 
 In [19]: 
 
     
 stan_utility.check_div(fit)
 

 
 
 

 
 


 
 
 202.0 of 4000 iterations ended with a divergen






Flashcard 2961914858764

    
	

	    
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#best-practice #pystan

	

    

    

    

    
	

	    
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Divergences can sometimes be [...]. 

	

    

    

    
	

	    
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		false positives
	    

	

    




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                    Divergences, however, can sometimes be false positives. To verify that we have real fitting issues we can rerun with a larger target acceptance probability,  adapt_delta , which will force more accurate simulations of Hamiltonian trajectori
Original toplevel document
pystan_workflow
nce (5.05%)
  Try running with larger adapt_delta to remove the divergences
 
 
 

 
 

 
 
 
 
 
 
 indicating that the Markov chains did not completely explore the posterior and that our Markov chain Monte Carlo estimators will be biased. 
 <span>Divergences, however, can sometimes be false positives.  To verify that we have real fitting issues we can rerun with a larger target acceptance probability,  adapt_delta , which will force more accurate simulations of Hamiltonian trajectories and reduce the false positives. 

 
 
 
 
 
 In [20]: 
 
     
 fit = model.sampling(data=data, seed=194838, control=dict(adapt_delta=0.9))
 

 
 
 

 
 
 
 
 
 
 Checking again, 

 
 
 
 
 
 In [21]: 
 
     
 sampler_params = fit.get_sam






Flashcard 2961917218060

    
	

	    
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#best-practice #pystan

	

    

    

    

    
	

	    
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With divergence, to verify that we have real fitting issues we can rerun with [...]

	

    

    

    
	

	    
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		a higher target acceptance rate
	    

	

    




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                    Divergences, however, can sometimes be false positives. To verify that we have real fitting issues we can rerun with a larger target acceptance probability,  adapt_delta , which will force more accurate simulations of Hamiltonian trajectories and reduce the false positives.  In [20]:  

Original toplevel document
pystan_workflow
nce (5.05%)
  Try running with larger adapt_delta to remove the divergences
 
 
 

 
 

 
 
 
 
 
 
 indicating that the Markov chains did not completely explore the posterior and that our Markov chain Monte Carlo estimators will be biased. 
 <span>Divergences, however, can sometimes be false positives.  To verify that we have real fitting issues we can rerun with a larger target acceptance probability,  adapt_delta , which will force more accurate simulations of Hamiltonian trajectories and reduce the false positives. 

 
 
 
 
 
 In [20]: 
 
     
 fit = model.sampling(data=data, seed=194838, control=dict(adapt_delta=0.9))
 

 
 
 

 
 
 
 
 
 
 Checking again, 

 
 
 
 
 
 In [21]: 
 
     
 sampler_params = fit.get_sam






Flashcard 2961919577356

    
	

	    
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#best-practice #pystan

	

    

    

    

    
	

	    
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a larger target acceptance probability will force [...] and reduce the false positive divergences

	

    

    

    
	

	    
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		more accurate simulations of Hamiltonian trajectories
	    

	

    




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                    Divergences, however, can sometimes be false positives. To verify that we have real fitting issues we can rerun with a larger target acceptance probability,  adapt_delta , which will force more accurate simulations of Hamiltonian trajectories and reduce the false positives.  In [20]:  
<html>
Original toplevel document
pystan_workflow
nce (5.05%)
  Try running with larger adapt_delta to remove the divergences
 
 
 

 
 

 
 
 
 
 
 
 indicating that the Markov chains did not completely explore the posterior and that our Markov chain Monte Carlo estimators will be biased. 
 <span>Divergences, however, can sometimes be false positives.  To verify that we have real fitting issues we can rerun with a larger target acceptance probability,  adapt_delta , which will force more accurate simulations of Hamiltonian trajectories and reduce the false positives. 

 
 
 
 
 
 In [20]: 
 
     
 fit = model.sampling(data=data, seed=194838, control=dict(adapt_delta=0.9))
 

 
 
 

 
 
 
 
 
 
 Checking again, 

 
 
 
 
 
 In [21]: 
 
     
 sampler_params = fit.get_sam






Flashcard 2961921936652

    
	

	    
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In order to argue that divergences are only false positives, the divergences have to be [...] for some adapt_delta sufficiently close to 1.

	

    

    

    
	

	    
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		completely eliminated
	    

	

    




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                    In order to argue that divergences are only false positives, the divergences have to be completely eliminated for some  adapt_delta  sufficiently close to 1. 

Original toplevel document
pystan_workflow

 
 

 
 


 
 
 45.0 of 4000 iterations ended with a divergence (1.125%)
  Try running with larger adapt_delta to remove the divergences
 
 
 

 
 

 
 
 
 
 
 
 we see that while the divergences were reduced they did not completely vanish.  <span>In order to argue that divergences are only false positives, the divergences have to be completely eliminated for some  adapt_delta  sufficiently close to 1.  Here we could continue increasing  adapt_delta , where we would see that the divergences do not completely vanish, or we can analyze the existing divergences graphically. 
 If the dive






Flashcard 2961923509516

    
	

	    
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#best-practice #pystan

	

    

    

    

    
	

	    
Question

	    
true divergences will tend to concentrate in [...]. 

	

    

    

    
	

	    
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		the pathological neighborhoods of the posterior
	    

	

    




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                    If the divergences are not false positives then they will tend to concentrate in the pathological neighborhoods of the posterior. Falsely positive divergent iterations, however, will follow the same distribution as non-divergent iterations. 
 

Original toplevel document
pystan_workflow
ompletely eliminated for some  adapt_delta  sufficiently close to 1.  Here we could continue increasing  adapt_delta , where we would see that the divergences do not completely vanish, or we can analyze the existing divergences graphically. 
 <span>If the divergences are not false positives then they will tend to concentrate in the pathological neighborhoods of the posterior.  Falsely positive divergent iterations, however, will follow the same distribution as non-divergent iterations. 
 Here we will use the  partition_div  function of the  stan_utility  module to separate divergence and non-divergent iterations, but note that this function works only if your model pa






Flashcard 2961925868812

    
	

	    
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#best-practice #pystan

	

    

    

    

    
	

	    
Question

	    
Graphically, falsely positive divergent iterations will [...].



 

	

    

    

    
	

	    
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		follow the same distribution as non-divergent iterations
	    

	

    




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                    If the divergences are not false positives then they will tend to concentrate in the pathological neighborhoods of the posterior. Falsely positive divergent iterations, however, will follow the same distribution as non-divergent iterations. 
 

Original toplevel document
pystan_workflow
ompletely eliminated for some  adapt_delta  sufficiently close to 1.  Here we could continue increasing  adapt_delta , where we would see that the divergences do not completely vanish, or we can analyze the existing divergences graphically. 
 <span>If the divergences are not false positives then they will tend to concentrate in the pathological neighborhoods of the posterior.  Falsely positive divergent iterations, however, will follow the same distribution as non-divergent iterations. 
 Here we will use the  partition_div  function of the  stan_utility  module to separate divergence and non-divergent iterations, but note that this function works only if your model pa






Flashcard 2961928228108

    
	

	    
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#best-practice #pystan

	

    

    

    

    
	

	    
Question

	    
One of the challenges with a visual analysis of divergences is determining [...]. 

	

    

    

    
	

	    
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		exactly which parameters to examine
	    

	

    




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                    One of the challenges with a visual analysis of divergences is determining exactly which parameters to examine. Consequently visual analyses are most useful when there are already components of the model about which you are suspicious 

Original toplevel document
pystan_workflow
      color = green, alpha=0.5)

plot.gca().set_xlabel("theta_1")
plot.gca().set_ylabel("tau")

plot.show()
 

 
 
 

 
 


 
 
 WARNING:root:`dtypes` ignored when `permuted` is False.
 
 
 

 


 

 

 

 
 

 
 
 
 
 
 
 <span>One of the challenges with a visual analysis of divergences is determining exactly which parameters to examine.  Consequently visual analyses are most useful when there are already components of the model about which you are suspicious, as in this case where we know that the correlation between random effects ( theta_1  through  theta_8 ) and the hierarchical standard deviation,  tau , can be problematic. 
 Indeed we 






Flashcard 2961930849548

    
	

	    
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#best-practice #pystan

	

    

    

    

    
	

	    
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The stan_utility module uses the E-BFMI threshold of [...] to diagnose problems

	

    

    

    
	

	    
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		0.2
	    

	

    




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                    The  stan_utility  module uses the threshold of 0.2 to diagnose problems 

Original toplevel document
pystan_workflow
ction of Missing Information, 

 
 
 
 
 
 In [18]: 
 
     
 stan_utility.check_energy(fit)
 

 
 
 

 
 


 
 
 Chain 2: E-BFMI = 0.177681346951
  E-BFMI below 0.2 indicates you may need to reparameterize your model
 
 
 

 
 

 
 
 
 
 
 
 <span>The  stan_utility  module uses the threshold of 0.2 to diagnose problems, although this is based on preliminary empirical studies and should be taken only as a very rough recommendation.  In particular, this diagnostic comes out of recent theoretical work an






Flashcard 2961933733132

    
	

	    
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#best-practice #pystan

	

    

    

    

    
	

	    
Question

	    
E-BFMI stands for [...],

	

    

    

    
	

	    
Answer

	    

		energy Bayesian Fraction of Missing Information
	    

	

    




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ory to explore another slice of the target parameter space. Unfortunately, the jumps between these slices induced by the momenta resamplings can be short, which often leads to slow exploration. 
 We can identify this problem by consulting the <span>energy Bayesian Fraction of Missing Information, 
<span><body><html>
Original toplevel document
pystan_workflow
.sampling(data=data, seed=194838, control=dict(max_treedepth=15)) 

 
 
 
 
 
 
 
 
 and then check if still saturated this larger threshold with 

 
 
 
 
 
 
 
 
 stan_utility.check_treedepth(fit, 15) 

 
 
 
 
 
 
 
 
 Checking the E-BFMI¶ <span>Hamiltonian Monte Carlo proceeds in two phases -- the algorithm first simulates a Hamiltonian trajectory that rapidly explores a slice of the target parameter space before resampling the auxiliary momenta to allow the next trajectory to explore another slice of the target parameter space.  Unfortunately, the jumps between these slices induced by the momenta resamplings can be short, which often leads to slow exploration. 
 We can identify this problem by consulting the energy Bayesian Fraction of Missing Information, 

 
 
 
 
 
 In [18]: 
 
     
 stan_utility.check_energy(fit)
 

 
 
 

 
 


 
 
 Chain 2: E-BFMI = 0.177681346951
  E-BFMI below 0.2 indicates you may need to reparameterize your mod






Flashcard 2961936092428

    
	

	    
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#best-practice #pystan

	

    

    

    

    
	

	    
Question

	    
Hamiltonian Monte Carlo proceeds in [...] phases 

	

    

    

    
	

	    
Answer

	    

		two
	    

	

    




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                    Hamiltonian Monte Carlo proceeds in two phases -- the algorithm first simulates a Hamiltonian trajectory that rapidly explores a slice of the target parameter space before resampling the auxiliary momenta to allow the next tr
Original toplevel document
pystan_workflow
.sampling(data=data, seed=194838, control=dict(max_treedepth=15)) 

 
 
 
 
 
 
 
 
 and then check if still saturated this larger threshold with 

 
 
 
 
 
 
 
 
 stan_utility.check_treedepth(fit, 15) 

 
 
 
 
 
 
 
 
 Checking the E-BFMI¶ <span>Hamiltonian Monte Carlo proceeds in two phases -- the algorithm first simulates a Hamiltonian trajectory that rapidly explores a slice of the target parameter space before resampling the auxiliary momenta to allow the next trajectory to explore another slice of the target parameter space.  Unfortunately, the jumps between these slices induced by the momenta resamplings can be short, which often leads to slow exploration. 
 We can identify this problem by consulting the energy Bayesian Fraction of Missing Information, 

 
 
 
 
 
 In [18]: 
 
     
 stan_utility.check_energy(fit)
 

 
 
 

 
 


 
 
 Chain 2: E-BFMI = 0.177681346951
  E-BFMI below 0.2 indicates you may need to reparameterize your mod






Flashcard 2961938451724

    
	

	    
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#best-practice #pystan

	

    

    

    

    
	

	    
Question

	    
The first phase of Hamiltonian Monte Carlo simulates a Hamiltonian trajectory that [...] 

	

    

    

    
	

	    
Answer

	    

		rapidly explores a slice of the target parameter space
	    

	

    




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                    Hamiltonian Monte Carlo proceeds in two phases -- the algorithm first simulates a Hamiltonian trajectory that rapidly explores a slice of the target parameter space before resampling the auxiliary momenta to allow the next trajectory to explore another slice of the target parameter space. Unfortunately, the jumps between these slices induced by the
Original toplevel document
pystan_workflow
.sampling(data=data, seed=194838, control=dict(max_treedepth=15)) 

 
 
 
 
 
 
 
 
 and then check if still saturated this larger threshold with 

 
 
 
 
 
 
 
 
 stan_utility.check_treedepth(fit, 15) 

 
 
 
 
 
 
 
 
 Checking the E-BFMI¶ <span>Hamiltonian Monte Carlo proceeds in two phases -- the algorithm first simulates a Hamiltonian trajectory that rapidly explores a slice of the target parameter space before resampling the auxiliary momenta to allow the next trajectory to explore another slice of the target parameter space.  Unfortunately, the jumps between these slices induced by the momenta resamplings can be short, which often leads to slow exploration. 
 We can identify this problem by consulting the energy Bayesian Fraction of Missing Information, 

 
 
 
 
 
 In [18]: 
 
     
 stan_utility.check_energy(fit)
 

 
 
 

 
 


 
 
 Chain 2: E-BFMI = 0.177681346951
  E-BFMI below 0.2 indicates you may need to reparameterize your mod






Flashcard 2961940811020

    
	

	    
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#best-practice #pystan

	

    

    

    

    
	

	    
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The second phase of Hamiltonian Monte Carlo [...] to allow the next trajectory to explore another slice of the target parameter space. 

	

    

    

    
	

	    
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		resamples the auxiliary momenta
	    

	

    




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                    Hamiltonian Monte Carlo proceeds in two phases -- the algorithm first simulates a Hamiltonian trajectory that rapidly explores a slice of the target parameter space before resampling the auxiliary momenta to allow the next trajectory to explore another slice of the target parameter space. Unfortunately, the jumps between these slices induced by the momenta resamplings can be short, which
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.sampling(data=data, seed=194838, control=dict(max_treedepth=15)) 

 
 
 
 
 
 
 
 
 and then check if still saturated this larger threshold with 

 
 
 
 
 
 
 
 
 stan_utility.check_treedepth(fit, 15) 

 
 
 
 
 
 
 
 
 Checking the E-BFMI¶ <span>Hamiltonian Monte Carlo proceeds in two phases -- the algorithm first simulates a Hamiltonian trajectory that rapidly explores a slice of the target parameter space before resampling the auxiliary momenta to allow the next trajectory to explore another slice of the target parameter space.  Unfortunately, the jumps between these slices induced by the momenta resamplings can be short, which often leads to slow exploration. 
 We can identify this problem by consulting the energy Bayesian Fraction of Missing Information, 

 
 
 
 
 
 In [18]: 
 
     
 stan_utility.check_energy(fit)
 

 
 
 

 
 


 
 
 Chain 2: E-BFMI = 0.177681346951
  E-BFMI below 0.2 indicates you may need to reparameterize your mod






Flashcard 2961943170316

    
	

	    
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#best-practice #pystan

	

    

    

    

    
	

	    
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Unfortunately, too short [...] induced by the momenta resamplings can lead to slow exploration.

	

    

    

    
	

	    
Answer

	    

		jumps between slices of trajectories
	    

	

    




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rst simulates a Hamiltonian trajectory that rapidly explores a slice of the target parameter space before resampling the auxiliary momenta to allow the next trajectory to explore another slice of the target parameter space. Unfortunately, the <span>jumps between these slices induced by the momenta resamplings can be short, which often leads to slow exploration. 
 We can identify this problem by consulting the energy Bayesian Fraction of Missing Information, 
<span><body><html>
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.sampling(data=data, seed=194838, control=dict(max_treedepth=15)) 

 
 
 
 
 
 
 
 
 and then check if still saturated this larger threshold with 

 
 
 
 
 
 
 
 
 stan_utility.check_treedepth(fit, 15) 

 
 
 
 
 
 
 
 
 Checking the E-BFMI¶ <span>Hamiltonian Monte Carlo proceeds in two phases -- the algorithm first simulates a Hamiltonian trajectory that rapidly explores a slice of the target parameter space before resampling the auxiliary momenta to allow the next trajectory to explore another slice of the target parameter space.  Unfortunately, the jumps between these slices induced by the momenta resamplings can be short, which often leads to slow exploration. 
 We can identify this problem by consulting the energy Bayesian Fraction of Missing Information, 

 
 
 
 
 
 In [18]: 
 
     
 stan_utility.check_energy(fit)
 

 
 
 

 
 


 
 
 Chain 2: E-BFMI = 0.177681346951
  E-BFMI below 0.2 indicates you may need to reparameterize your mod






Flashcard 2961945529612

    
	

	    
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#best-practice #pystan

	

    

    

    

    
	

	    
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The dynamic implementation of Hamiltonian Monte Carlo used in Stan has a [...] built in to avoid infinite loops that can occur for non-identified models. 

	

    

    

    
	

	    
Answer

	    

		maximum trajectory length
	    

	

    




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                    The dynamic implementation of Hamiltonian Monte Carlo used in Stan has a maximum trajectory length built in to avoid infinite loops that can occur for non-identified models. For sufficiently complex models, however, Stan can saturate this threshold even if the model is identified, wh
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agnostics that can indicate problems with the fit.
These diagnostics are extremely sensitive and typically indicate problems
long before the arise in the more universal diagnostics considered above. 

 
 
 
 
 
 
 
 
 Checking the Tree Depth¶ <span>The dynamic implementation of Hamiltonian Monte Carlo used in Stan has a maximum trajectory length built in to avoid infinite loops that can occur for non-identified models.  For sufficiently complex models, however, Stan can saturate this threshold even if the model is identified, which limits the efficacy of the sampler. 
 We can check whether that threshold was hit using one of our utility functions, 

 
 
 
 
 
 In [17]: 
 
     
 stan_utility.check_treedepth(fit)
 

 
 
 

 
 


 
 
 0 of 4000 iterat






Flashcard 2961947888908

    
	

	    
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#best-practice #pystan

	

    

    

    

    
	

	    
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The dynamic implementation of Hamiltonian Monte Carlo used in Stan has a maximum trajectory length built in to avoid  [...] . 

	

    

    

    
	

	    
Answer

	    

		possible infinite loops in non-identified models
	    

	

    




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                    The dynamic implementation of Hamiltonian Monte Carlo used in Stan has a maximum trajectory length built in to avoid infinite loops that can occur for non-identified models. For sufficiently complex models, however, Stan can saturate this threshold even if the model is identified, wh
Original toplevel document
pystan_workflow
agnostics that can indicate problems with the fit.
These diagnostics are extremely sensitive and typically indicate problems
long before the arise in the more universal diagnostics considered above. 

 
 
 
 
 
 
 
 
 Checking the Tree Depth¶ <span>The dynamic implementation of Hamiltonian Monte Carlo used in Stan has a maximum trajectory length built in to avoid infinite loops that can occur for non-identified models.  For sufficiently complex models, however, Stan can saturate this threshold even if the model is identified, which limits the efficacy of the sampler. 
 We can check whether that threshold was hit using one of our utility functions, 

 
 
 
 
 
 In [17]: 
 
     
 stan_utility.check_treedepth(fit)
 

 
 
 

 
 


 
 
 0 of 4000 iterat






Flashcard 2961951296780

    
	

	    
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#best-practice #pystan

	

    

    

    

    
	

	    
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Split \( \hat{R} \) quantifies an important necessary condition for [...]

	

    

    

    
	

	    
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		geometric ergodicity
	    

	

    




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                    Split R̂  quantifies an important necessary condition for geometric ergodicity 

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Flashcard 2961952869644

    
	

	    
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Improving the mixing of the Markov chains almost always requires [...]

	

    

    

    
	

	    
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		tweaking the model specification



for example with a reparameterization or stronger priors.
	    

	

    




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>
                    Both large split R ̂ R^ \hat{R} and low effective sample size per iteration are
consequences of poorly mixing Markov chains. Improving the mixing of the
Markov chains almost always requires tweaking the model specification, for
example with a reparameterization or stronger priors. 
<html>
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Flashcard 2961955228940

    
	

	    
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[...] quantifies the accuracy of the Markov chain Monte Carlo estimator of a given function, e.g. parameter mean

	

    

    

    
	

	    
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		the effective sample size
	    

	

    




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                    the effective sample size quantifies the accuracy
of the Markov chain Monte Carlo estimator of a given function, here each
parameter mean, provided that geometric ergodicity holds. The potential
problem with the
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 chains (at 
convergence, Rhat=1).
 
 
 

 
 

 
 
 
 
 
 
 We can investigate each more programatically, however, using some of our
utility functions. 

 
 
 
 
 
 
 
 
 Checking Split R̂ R^ and Effective Sample Sizes¶ As noted in Section 1, <span>the effective sample size quantifies the accuracy
of the Markov chain Monte Carlo estimator of a given function, here each
parameter mean, provided that geometric ergodicity holds.  The potential
problem with these effective sample sizes, however, is that we must
estimate them from the fit output.  When we geneate less than 0.001
effective samples per transition of the Markov chain the estimators that
we use are typically biased and can significantly overestimate the true
effective sample size. 
 We can check that our effective sample size per iteration is large enough
with one of our utility functions, 

 
 
 
 
 
 In [14]: 
 
     
 stan_utility.check_n_eff(fit)
 

 
 
 

 







Flashcard 2961957588236

    
	

	    
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#betancourt #probability-theory

	

    

    

    

    
	

	    
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we cannot explicitly construct [...] in any meaningful sense. Instead we must utilize problem-specific representations of it

	

    

    

    
	

	    
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		abstract probability distributions
	    

	

    




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                    we cannot explicitly construct abstract probability distributions in any meaningful sense. Instead we must utilize problem-specific representations of abstract probability distributions 

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Probability Theory (For Scientists and Engineers)
robability theory. 
 Let me open with a warning that the section on abstract probability theory will be devoid of any concrete examples. This is not because of any conspiracy to confuse the reader, but rather is a consequence of the fact that <span>we cannot explicitly construct abstract probability distributions in any meaningful sense. Instead we must utilize problem-specific representations of abstract probability distributions which means that concrete examples will have to wait until we introduce these representations in Section 3. 
 
 1 Setting A Foundation 
 Ultimately probability theory concerns itself wi






Flashcard 2961959947532

    
	

	    
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#betancourt #probability-theory

	

    

    

    

    
	

	    
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many introductions to probability theory sloppily confound [...with...]

	

    

    

    
	

	    
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		the abstract mathematics with their practical implementations
	    

	

    




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                    In particular, many introductions to probability theory sloppily confound the abstract mathematics with their practical implementations, convoluting what we can calculate in the theory with how we perform those calculations. To make matters even worse, probability theory is used to model a variety of subtlety different 
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Probability Theory (For Scientists and Engineers)
ity theory is a rich and complex field of mathematics with a reputation for being confusing if not outright impenetrable. Much of that intimidation, however, is due not to the abstract mathematics but rather how they are employed in practice. <span>In particular, many introductions to probability theory sloppily confound the abstract mathematics with their practical implementations, convoluting what we can calculate in the theory with how we perform those calculations. To make matters even worse, probability theory is used to model a variety of subtlety different systems, which then burdens the already confused mathematics with the distinct and often conflicting philosophical connotations of those applications. 
 In this case study I attempt to untangle this pedagogical knot to illuminate the basic concepts and manipulations of probability theory. Our ultimate goal is to demystify what we can 






Flashcard 2961962306828

    
	

	    
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#betancourt #probability-theory

	

    

    

    

    
	

	    
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 many introductions to probability theory sloppily confound the abstract mathematics with their practical implementations, convoluting [...with...]. 

	

    

    

    
	

	    
Answer

	    

		what we can calculate in the theory with how we perform those calculations in practice
	    

	

    




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                    In particular, many introductions to probability theory sloppily confound the abstract mathematics with their practical implementations, convoluting what we can calculate in the theory with how we perform those calculations. To make matters even worse, probability theory is used to model a variety of subtlety different systems, which then burdens the already confused mathematics with the distinct and often
Original toplevel document
Probability Theory (For Scientists and Engineers)
ity theory is a rich and complex field of mathematics with a reputation for being confusing if not outright impenetrable. Much of that intimidation, however, is due not to the abstract mathematics but rather how they are employed in practice. <span>In particular, many introductions to probability theory sloppily confound the abstract mathematics with their practical implementations, convoluting what we can calculate in the theory with how we perform those calculations. To make matters even worse, probability theory is used to model a variety of subtlety different systems, which then burdens the already confused mathematics with the distinct and often conflicting philosophical connotations of those applications. 
 In this case study I attempt to untangle this pedagogical knot to illuminate the basic concepts and manipulations of probability theory. Our ultimate goal is to demystify what we can 






Flashcard 2961964666124

    
	

	    
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#betancourt #probability-theory

	

    

    

    

    
	

	    
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probability theory is often used to model a variety of subtlely different systems, which then burdens the already confused mathematics with  [...] .

	

    

    

    
	

	    
Answer

	    

		the distinct and often conflicting philosophical connotations of those applications
	    

	

    




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ppily confound the abstract mathematics with their practical implementations, convoluting what we can calculate in the theory with how we perform those calculations. To make matters even worse, probability theory is used to model a variety of <span>subtlety different systems, which then burdens the already confused mathematics with the distinct and often conflicting philosophical connotations of those applications. 
<span><body><html>
Original toplevel document
Probability Theory (For Scientists and Engineers)
ity theory is a rich and complex field of mathematics with a reputation for being confusing if not outright impenetrable. Much of that intimidation, however, is due not to the abstract mathematics but rather how they are employed in practice. <span>In particular, many introductions to probability theory sloppily confound the abstract mathematics with their practical implementations, convoluting what we can calculate in the theory with how we perform those calculations. To make matters even worse, probability theory is used to model a variety of subtlety different systems, which then burdens the already confused mathematics with the distinct and often conflicting philosophical connotations of those applications. 
 In this case study I attempt to untangle this pedagogical knot to illuminate the basic concepts and manipulations of probability theory. Our ultimate goal is to demystify what we can 






Flashcard 2961980394764

    
	

	    
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#best-practice #pystan

	

    

    

    

    
	

	    
Question

	    
The second phase of Hamiltonian Monte Carlo resample the auxiliary momenta to allow the next trajectory to  [...] . 

	

    

    

    
	

	    
Answer

	    

		explore another slice of the target parameter space
	    

	

    




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                    Hamiltonian Monte Carlo proceeds in two phases -- the algorithm first simulates a Hamiltonian trajectory that rapidly explores a slice of the target parameter space before resampling the auxiliary momenta to allow the next trajectory to explore another slice of the target parameter space. Unfortunately, the jumps between these slices induced by the momenta resamplings can be short, which
Original toplevel document
pystan_workflow
.sampling(data=data, seed=194838, control=dict(max_treedepth=15)) 

 
 
 
 
 
 
 
 
 and then check if still saturated this larger threshold with 

 
 
 
 
 
 
 
 
 stan_utility.check_treedepth(fit, 15) 

 
 
 
 
 
 
 
 
 Checking the E-BFMI¶ <span>Hamiltonian Monte Carlo proceeds in two phases -- the algorithm first simulates a Hamiltonian trajectory that rapidly explores a slice of the target parameter space before resampling the auxiliary momenta to allow the next trajectory to explore another slice of the target parameter space.  Unfortunately, the jumps between these slices induced by the momenta resamplings can be short, which often leads to slow exploration. 
 We can identify this problem by consulting the energy Bayesian Fraction of Missing Information, 

 
 
 
 
 
 In [18]: 
 
     
 stan_utility.check_energy(fit)
 

 
 
 

 
 


 
 
 Chain 2: E-BFMI = 0.177681346951
  E-BFMI below 0.2 indicates you may need to reparameterize your mod






Flashcard 2961983016204

    
	

	    
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#best-practice #pystan

	

    

    

    

    
	

	    
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In Stan a larger target acceptance probability is set by the keyword [...]

	

    

    

    
	

	    
Answer

	    

		adapt_delta
	    

	

    




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                    Divergences, however, can sometimes be false positives. To verify that we have real fitting issues we can rerun with a larger target acceptance probability,  adapt_delta , which will force more accurate simulations of Hamiltonian trajectories and reduce the false positives.  In [20]:  

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nce (5.05%)
  Try running with larger adapt_delta to remove the divergences
 
 
 

 
 

 
 
 
 
 
 
 indicating that the Markov chains did not completely explore the posterior and that our Markov chain Monte Carlo estimators will be biased. 
 <span>Divergences, however, can sometimes be false positives.  To verify that we have real fitting issues we can rerun with a larger target acceptance probability,  adapt_delta , which will force more accurate simulations of Hamiltonian trajectories and reduce the false positives. 

 
 
 
 
 
 In [20]: 
 
     
 fit = model.sampling(data=data, seed=194838, control=dict(adapt_delta=0.9))
 

 
 
 

 
 
 
 
 
 
 Checking again, 

 
 
 
 
 
 In [21]: 
 
     
 sampler_params = fit.get_sam